On the number of mutually disjoint isomorphic (nu, kappa, gamma) designs

Gray, Ken and Street, Anne P. (2010) On the number of mutually disjoint isomorphic (nu, kappa, gamma) designs. Bulletin of the Institute of Combinatorics and its Applications, 60 9-14.

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Author Gray, Ken
Street, Anne P.
Title On the number of mutually disjoint isomorphic (nu, kappa, gamma) designs
Formatted title
On the number of mutually disjoint isomorphic (ν, κ, λ) designs
Journal name Bulletin of the Institute of Combinatorics and its Applications
ISSN 1183-1278
Publication date 2010
Sub-type Article (original research)
Volume 60
Start page 9
End page 14
Total pages 6
Place of publication Winnipeg, MB, Canada
Publisher The Institute of Combinatorics & Its Applications (ICA)
Collection year 2011
Language eng
Formatted abstract
This paper uses a simple counting argument to obtain an expression in ν, κ, λ providing a lower bound on the number of mutually disjoint, isomorphic (ν, κ, λ) designs, where we can assume ν ≥ 2k.
First, for those particular designs with κ ≥ 4, this lower bound confirms a previous result obtained in a different way by others, namely that, for a design such as a (ν, κ, 1) design, D, with κ ≥ 3, there exists another design isomorphic to, and disjoint from, D. Secondly, it provides information about how many mutually disjoint isomorphic (ν, κ, λ) designs must exist when k ≥ 4 and A mayor may not be 1. Finally, for a given κ ≥ 4, the bound is shown to increase as ν increases.
Keyword Balanced incomplete block designs
Mutually disjoint designs
Isomorphic designs
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2011 Collection
 
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Created: Thu, 24 Feb 2011, 12:54:08 EST by Kay Mackie on behalf of School of Mathematics & Physics